Sentence examples for exist provided that from inspiring English sources

We prove that they exist provided that the lengths of the sub-spans are properly chosen.

Although the associated function lacks continuity at some points, it is demonstrated that an equilibrium must exist provided that the parking capacity suffices to accommodate the demand volumes.

Socioeconomic inequalities may exist, provided that this inequality is in everyone's favor and does not harm society as a whole (the famous 'difference principle').

General bounds on the exact eigenvalues of the transcendental eigenvalue problem provided by the quadratic matrix pencil are shown to exist, provided that the three fixed values are below the lowest pole of the transcendental stiffness matrix considered and that the three coefficient matrices are positive definite.

In particular, we prove that ε → 1 / 2 as k → 0. Taking advantage of these results, the analysis of a bridge with two symmetrically-placed piers ( N = 3 ) is performed in Section 2.3, where buckled static solutions are proved to exist provided that | I 1 | = | I 3 | ≠ | I 2 | fulfills a suitable condition.

Two of the three typical responses shown in Figure 1 exhibit a positive deflection of the membrane potential characterised by a 'hump' in the time trace of the membrane potential at the end of the burst; this is called after-depolarisation (ADP), which can exist provided that τ m FO < τ m SI [13].

It has been shown that an endemic equilibrium exists provided that (R_{v}>1).

We also observe that the inverse of in the ML estimator (16) exists provided that is full rank and.

An endemic equilibrium (E^(S^, V^,I^)) exists provided that (R_{v} >1).

A GNE in the game G exists provided that the K sets A k ( p ∖ k ) ⊆ P k, k ∈ K, are nonempty, which translates, using (19), into ensuring that there exists at least a power level π k ( q ) ∈ P k such that π k ( q ) ≥ γ req / ν k ( p ∖ k ) for all k.

Such bursts will continue to appear as long as the DNA damage exists (provided that the cell remains alive).